Given a Binary Tree, the task is to find the size of largest Perfect sub-tree in the given Binary Tree.
Perfect Binary Tree – A Binary tree is Perfect Binary Tree in which all internal nodes have two children and all leaves are at the same level.
Input: 1 / \ 2 3 / \ / 4 5 6 Output: Size : 3 Inorder Traversal : 4 2 5 The following sub-tree is the maximum size Perfect sub-tree 2 / \ 4 5 Input: 50 / \ 30 60 / \ / \ 5 20 45 70 / \ / \ 10 85 65 80 Output: Size : 7 Inorder Traversal : 10 45 85 60 65 70 80
Approach: Simply traverse the tree in bottom up manner. Then on coming up in recursion from child to parent, we can pass information about sub-trees to the parent. The passed information can be used by the parent to do Prefect Tree test (for parent node) only in constant time. A left sub-tree need to tell the parent whether it is a Perfect Binary Tree or not and also need to pass max height of the Perfect Binary Tree coming from left child. Similarly, the right sub-tree also needs to pass max height of Prefect Binary Tree coming from right child.
The sub-trees need to pass the following information up the tree for finding the largest Perfect sub-tree so that we can compare the maximum height with the parent’s data to check the Perfect Binary Tree property.
- There is a bool variable to check whether the left child or the right child sub-tree is Perfect or not.
- From left and right child calls in recursion we find out if parent sub-tree if Prefect or not by following 2 cases:
- If both left child and right child are perfect binary tree and have same heights then parent is also a Perfect Binary Tree with height plus one of its child.
- If the above case is not true then parent cannot be perfect binary tree and simply returns max size Perfect Binary Tree coming from left or right sub-tree by comparing their heights.
Below is the implementation of the above approach:
Size : 3 Inorder Traversal : 4 2 5
- Find the largest BST subtree in a given Binary Tree | Set 1
- Find the largest Complete Subtree in a given Binary Tree
- Find largest subtree sum in a tree
- Find sum of all nodes of the given perfect binary tree
- Queries to find the maximum Xor value between X and the nodes of a given level of a perfect binary tree
- Subtree with given sum in a Binary Tree
- Check if a binary tree is subtree of another binary tree | Set 1
- Check if a binary tree is subtree of another binary tree | Set 2
- Duplicate subtree in Binary Tree | SET 2
- Check if the given Binary Tree have a Subtree with equal no of 1's and 0's
- Find largest subtree having identical left and right subtrees
- Convert a Binary Tree such that every node stores the sum of all nodes in its right subtree
- Construct XOR tree by Given leaf nodes of Perfect Binary Tree
- Change a Binary Tree so that every node stores sum of all nodes in left subtree
- Find the Kth node in the DFS traversal of a given subtree in a Tree
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